Theoretical study of the photoabsorption spectrum of ${\mathrm{Na}}_8$, ${\mathrm{Na}}_{20}$, ${\mathrm{Cs}}_8$, and ${\mathrm{Cs}}_{10}$O clusters

We have used the spherically-averaged-pseudopotential model to study, within the time-dependent density-functional theory, the response to light ${\mathrm{Na}}_8$, ${\mathrm{Na}}_{20}$, ${\mathrm{Cs}}_8$, and ${\mathrm{Cs}}_{10}$O clusters. The influence of electronic and geometrical effects has been analyzed by comparing our results to experiment and with other available calculations. From this analysis we conclude (1) the position of the surface plasmon in the photoabsorption spectrum depends mainly on the cluster size; (2) the two-peak structure of the photoabsorption spectrum of ${\mathrm{Na}}_{20}$, ${\mathrm{Cs}}_8$, and ${\mathrm{Cs}}_{10}$O originates from the coupling of the collective mode (surface plasmon) with a particle-hole transition; (3) in the cases of ${\mathrm{Cs}}_8$ and ${\mathrm{Cs}}_{10}$O the geometries which lead to agreement with experiment are such that Cs atoms are absent from the cluster center; and (4) the particle-hole transition responsible for the plasmon fragmentation in ${\mathrm{Cs}}_{10}$O involves a p-type electronic level with partial oxygen character, contrary to the picture of treating ${\mathrm{Cs}}_{10}$O as a system with only eight active electrons.